Surface-mediated frequency aging beyond quality-factor saturation in an AlScN-on-silicon resonator

Timekeeping is the invisible architecture of modern life, holding together everything from the GPS in a car to the synchronization of global financial networks. For decades, the most precise clocks have relied on the vibrations of atoms, but these devices are often large, power-hungry, and difficult to scale down for everyday use. Engineers have spent years trying to replace these atomic standards with tiny mechanical resonators—microscopic structures that vibrate at a specific, steady rhythm, much like a tuning fork. These tiny machines are made of silicon and piezoelectric films, materials that can convert electrical signals into mechanical motion and back again. The goal is to create a clock that is small enough to fit on a chip yet stable enough to keep time for days without drifting. However, as these devices shrink, they become increasingly sensitive to their environment. The air trapped inside the tiny package that seals the device can interfere with the vibration, and the surfaces of the device itself can slowly change over time, causing the clock to lose its accuracy. Understanding exactly how these tiny structures interact with the gas around them is the key to building the next generation of reliable, miniature timekeepers.

Researchers at the University of Michigan recently set out to untangle a specific mystery in this field: how does the air pressure inside a vacuum package affect the two most important characteristics of a mechanical clock? They focused on a device made of aluminum scandium nitride on a silicon base, a resonator that vibrates at 64.21 million times per second. In the world of these devices, scientists traditionally measure two things to judge if a package is good enough for a precision clock. The first is the "quality factor," a number that tells engineers how much energy the device loses to friction with the surrounding gas. The second is the resonance frequency, the actual speed at which the device vibrates. For years, the industry standard has been to assume that if the quality factor stops changing as the vacuum gets better, the package is sealed and stable. The logic was that once the gas damping stops affecting the energy loss, the clock is safe. But the new study suggests this assumption is dangerously incomplete.

The team placed their resonator inside a chamber where they could precisely control the pressure, ranging from a near-perfect vacuum up to normal atmospheric pressure. They watched how the device behaved as they stepped the pressure down and then back up again. What they found was a clear separation between the behavior of the energy loss and the behavior of the vibration speed. When the pressure changed, the energy loss, measured by the quality factor, settled down almost immediately. It reached a steady state that depended only on the current pressure and did not remember what the pressure had been before. Once the pressure dropped below about 1 Torr, the quality factor hit a ceiling and stopped changing, suggesting that the gas was no longer a significant source of friction.

However, the vibration speed told a completely different story. Even when the pressure had stabilized and the energy loss had stopped changing, the vibration speed continued to drift for hours. The device seemed to be slowly adjusting to the new environment, with its frequency shifting as gas molecules attached to or detached from the surface of the silicon. This process was so slow that even after the pressure was held constant for ten minutes, the frequency was still moving. The researchers observed that the frequency continued to change measurably down to pressures as low as 0.00001 Torr, a level far lower than the point where the energy loss had stopped changing. In fact, a single step in pressure could cause the frequency to shift by an amount equivalent to nearly two parts per million, a change that would accumulate into a significant timing error over time.

To understand why this was happening, the team looked at how the frequency changed over time after a pressure step. They found that the shifts did not follow a simple, predictable curve. Instead, the relaxation process was complex, involving a wide variety of speeds as different molecules on the surface settled into place. This behavior indicated that the surface of the device was not a uniform, static object but a dynamic landscape where molecules were constantly rearranging. The researchers also tested the device at a specific temperature where the natural drift caused by heat was canceled out, ensuring that the changes they saw were truly due to the gas and not temperature fluctuations. They confirmed that the frequency continued to evolve for hours, long after the gas damping had reached a steady state.

The implications of this discovery are significant for anyone trying to build a precise mechanical clock. The study proves that a package can appear to be a perfect vacuum based on how much energy the device loses, yet still be chemically active enough to ruin the clock's accuracy. The quality factor, which has long been the gold standard for judging vacuum integrity, is not enough on its own. A package might look stable because the gas friction has stopped changing, but the surface of the device might still be slowly absorbing or releasing molecules, causing the clock to age and drift. The researchers found that to achieve long-term stability, the vacuum level needs to be much higher than previously thought, and the package design must account for these slow surface changes.

In their final tests, the team tracked the device for ten hours at different pressures to see how these slow changes affected the clock's ability to keep time. At normal atmospheric pressure, the gas friction made the clock jittery and less stable in the short term. But at lower pressures, where the gas friction was low, a different problem emerged. The slow, deterministic drift of the frequency, caused by the surface molecules rearranging themselves, became the dominant source of error over longer periods. This drift was so persistent that it overwhelmed the random noise of the system, making the clock less reliable over time even in a good vacuum. The study concludes that for these tiny mechanical clocks to reach the stability of atomic standards, engineers must look beyond just the pressure inside the package. They must also control the chemistry of the surfaces inside, ensuring that the materials do not slowly change their state over hours or days. The path to a perfect miniature clock requires not just a vacuum, but a surface that remains perfectly still.